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Popular >

derivative of e^x(7x^2-14x+14)

Solution

derivative of

e^{x} (7 x^{2} - 14 x + 14)

Solution

7 e^{x} x^{2}

Solution steps

\frac{d}{d x} (e^{x} (7 x^{2} - 14 x + 14))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = 7 x^{2} - 14 x + 14

= \frac{d}{d x} (e^{x}) (7 x^{2} - 14 x + 14) + \frac{d}{d x} (7 x^{2} - 14 x + 14) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (7 x^{2} - 14 x + 14) = 14 x - 14

= e^{x} (7 x^{2} - 14 x + 14) + (14 x - 14) e^{x}

Simplify

e^{x} (7 x^{2} - 14 x + 14) + (14 x - 14) e^{x} : 7 e^{x} x^{2}

= 7 e^{x} x^{2}

Popular Examples

tangent of 4/(x^2)-1/(sqrt(x))tangent of

\frac{4}{x ^{2}} - \frac{1}{x}

(d^2)/(dx^2)(1/(sqrt(1-x^2)))

\frac{d ^{2}}{d x ^{2}} (\frac{1}{1 - x ^{2}})

integral of 2yarctan(x)

\int 2 y arctan (x) d y

y^{''}-2y^'-24y=0,y(0)=-1,y^'(0)=14

y^{^{''}} - 2 y^{^{'}} - 24 y = 0, y (0) = - 1, y^{^{'}} (0) = 14

integral of ((x^3))/((sqrt(x^4+5)))

\int \frac{( x ^{3} )}{( x ^{4} + 5 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of e^x(7x^2-14x+14) ?
The derivative of e^x(7x^2-14x+14) is 7e^xx^2
What is the first derivative of e^x(7x^2-14x+14) ?
The first derivative of e^x(7x^2-14x+14) is 7e^xx^2